Single Atom Adhesion in Optimized Gold Nanojunctions

We study the interaction between single apex atoms in a metallic contact, using the break junction geometry. By carefully training our samples, we create stable junctions in which no further atomic reorganization takes place. This allows us to study the relation between the so-called jump out of contact (from contact to tunneling regime) and jump to contact (from tunneling to contact regime) in detail. Our data can be fully understood within a relatively simple elastic model, where the elasticity $k$ of the electrodes is the only free parameter. We find $5<k<32\mathrm{N}/\mathrm{m}$. Furthermore, the interaction between the two apex atoms on both electrodes, observed as a change of slope in the tunneling regime, is accounted for by the same model.

Figure 1

Points: conductance $G$ vs distance $\mathrm{D}$ for four successive $G_0$ loops ($V_{\mathrm{bias}}=50\mathrm{mV}$). The jump to contact occurs at $\mathrm{D}=1.5\AA$; the jump out of contact at $\mathrm{D}=2.0\AA$. Black line: fit to model in Fig. 2 ($k=15.7\mathrm{N}/\mathrm{m}$). For the other parameters we use literature values: $F_0=1.5\mathrm{nN}$, $d=2.5\AA$, and $E_b=0.7\mathrm{eV}$. The work function, $\varphi =5\mathrm{eV}$, was measured independently. Inset graph: zoom of $G$ vs $\mathrm{D}$ in contact regime (linear scale). Picture: scanning electron micrograph of a lithographic break junction.

Figure 2

Total energy as a function of the interatomic distance $x$ of a gold dimer, for different electrode separations $\mathrm{D}$ (see inset; ${\mathrm{D}}_0$ denotes an offset distance). Two contributions are included: one due to the springs (spring constant $k$) and one due to the dimer (described by the “universal” binding curve). Depending on $\mathrm{D}$, the total energy may have two minima. For the atom to jump in and out of contact, a barrier has to be overcome. Hence, opening and closing occurs at different positions, explaining the hysteresis in $G_0$ loops. Note: same parameters as in Fig. 1.

Figure 3

(a) Conductance $G$ just before JC ($G_a$) vs $G$ just after JOC ($G_d$) for 734 different $G_0$ loops. (b) Average $G_a$ as a function of $G_d$. Averaging is done within regular bins of $G_d$, as indicated in (a). The line is a fit to the model, assuming a varying spring constant $5<k<32\mathrm{N}/\mathrm{m}$. The other parameters are the same as in Figs. 1, 2.

Figure 4

(a) Conductance just before JOC ($G_c$) vs $G$ just after JC ($G_b$) for 734 different $G_0$ loops. The dashed line represents $G_c=G_b$. Inset: schematic junction; scale bar: barrier length for tunneling.